Question

Alex and his friends played a spin wheel game. From the given data set, how would the median change if 5 is added to every number?

• A. It will increase.
• B. It will decrease.
• C. It will be equal.
• D. It will double the original value.

Answer 1

The correct option is A It will increase.

The given data set is

4, 7, 11, 14, 12, 6, 5, 13

Total number of data = 8

For a set with an even number of values, the median is the mean of the two middle values.

If we arrange the data set in ascending order, we get

4, 5, 6, 7, 11, 12, 13, 14

Here, the middle values are 7 and 11.

Median = $\frac{7+11}{2}$

= $\frac{18}{2}$

= 9

$\therefore$ Median = 9

Adding 5 to all the numbers, we get

4+5, 5+5, 6+5, 7+5, 11+5, 12+5, 13+5, 14+5

9, 10, 11, 12, 16, 17, 18, 19

Here, the middle values are 12 and 16.

Median = $\frac{12+16}{2}$

= $\frac{28}{2}$

= 14

$\therefore$ The new median is 14.

The old median is 9 and the new median is 14.

Here, the new median is greater than the old median.

Hence, the median will increase, if we add 5 to every number.